CYK tensors, Maxwell field and conserved quantities for the spin-2 field

Starting from an important application of conformal Yano-Killing tensors for the existence of global charges in gravity, (which has been performed in [ 17] and [18]), some new observations at I+ are given. They allow us to define asymptotic charges (at future null infinity) in-terms of the Weyl tensor together with their fluxes through I+. It happens that some of them play the role of obstructions for the existence of angular momentum. Moreover, new relations between solutions of the Maxwell equations and the spin-2 field are given. They are used in the construction of new conserved quantities which are quadratic in terms of the Weyl tensor. The formulae obtained are similar to the functionals obtained from the Bel-Robinson tensor.